MathDB

Tow circumferences of radius

R_1

and

R_2

are tangent externally between each other. Besides that, they are both tangent to a semicircle with radius of 1, as shown in the figure. (Diagram is in the attachment)
a) If

A_1

and

A_2

are the tangency points of the two circumferences with the diameter of the semicircle, find the length of

\overline{A_1 A_2}

.
b) Prove that

R_{1}+R_{2}=2\sqrt{R_{1}R_{2}}(\sqrt{2}-\sqrt{R_{1}R_{2}})

Problem Statement